Skip to main content
Log in

Graph rigidity and localization of multi-robot formations

  • Computer & Information Science
  • Published:
Journal of Zhejiang University-SCIENCE A Aims and scope Submit manuscript

Abstract

This paper provides theoretical foundation for the problem of localization in multi-robot formations. Sufficient and necessary conditions for completely localizing a formation of mobile robots/vehicles in SE(2) based on distributed sensor networks and graph rigidity are proposed. A method for estimating the quality of localizations via a linearized weighted least-squares algorithm is presented, which considers incomplete and noisy sensory information. The approach in this paper had been implemented in a multi-robot system of five car-like robots equipped with omni-directional cameras and IEEE 802.11b wireless network.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Belta, C., Kumar, V., 2001. Motion Generation for Formation of Robots: A Geometric Approach. Proc. of Intl. Conf. on Robotics and Automation, Seoul, Korea.

  • Das, A., Spletzer, J., Kumar, V., Taylor, C., 2002. Ad Hoc Networks for Localization and Control. Proc. of the 41st IEEE Conf. on Decision and Control, Las Vegas, NV.

  • Desai, A., Kumar, V., Ostrowski, J., 2001. A Theoretical Framework for Modeling and Controlling Formation of Mobile Robot. IEEE Transactions on Robotics and Automations.

  • Eren, T., Belhumeur P.N., Anderson B.D.O., Morse, A.S., 2002. A Framework for Maintaining Formations based on Rigidity. Proceedings of the IFAC Congress, p. 2752–2757.

  • Eren, T., Goldenberg, D., Whiteley, W., Yang, Y.R., Morse, A.S., Anderson, B.D.O., Belhumeur, P.N., 2004. Rigidity and Randomness in Network Localization. Proc. of the IEEE INFOCOM Conference, Hong Kong.

  • Howard, A., Matari, M., Sukhatme, C., 2002. Team Localization: A Maximum Likelihood Approach. Technical Report IRIS-01-415, Institute for Robotics and Intelligent Systems Technical Report, University of Southern California.

  • Laman, G., 1970. On graphs and rigidity of plane skeletal structures.Journal of Engineering Mathematics,4: 331–340.

    Article  MathSciNet  MATH  Google Scholar 

  • Olfati-Saber, R., Murray, R.M., 2002. Graph Rigidity and Distributed Formation Stabilization of Multi-vehicle systems. Proc. of the 41st IEEE Conf. on Dicision and Control, Las Vegas, NV.

  • Pappas, G.J., Tabuada P., Lima, P., 2001. Feasible Formations of Multi-agent Systems. Proceedings of the American Control Conference, Arlington, Virginia.

  • Roth, B., 1982. Rigidity and flexible frameworks.The American Mathematical Monthly,88: 6–21.

    Article  MATH  Google Scholar 

  • Roumeliotis, S., Bekey, G., 2000. Collective Localization: A Distributed Kalman Filter Approach to Localization of Groups of Mobile Robots. Proc. of the IEEE Intl. Conf. on Robotics and Automation, San Francisco, p. 2958–2965.

  • Spletzer, J., Taylor, C.J., 2003. Dynamic sensor planning and control for optimally tracking targets.International Journal of Robotics Research,22: 7–20.

    Article  Google Scholar 

  • Whiteley, W., Tay, T., 1985. Generating isostatic frameworks.Structural Topology,11: 21–69.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhang Fan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, F. Graph rigidity and localization of multi-robot formations. J. Zheijang Univ.-Sci. 5, 558–566 (2004). https://doi.org/10.1631/jzus.2004.0558

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1631/jzus.2004.0558

Key words

Document code

CLC number

Navigation